Deep brain stimulation pulse sequences to optimally modulate frequency-specific neural activity

Abstract

Precise neuromodulation systems are needed to identify the role of neural oscillatory dynamics in brain function, and to advance the development of electrical stimulation therapies tailored to each patient’s signature of brain dysfunction. Low-frequency, local field potentials (LFPs) are of increasing interest for the development of these systems because they reflect the synaptic inputs to a recorded neuronal population and can be chronically recorded in humans. Here, we identified stimulation pulse sequences to optimally minimize or maximize the 2-norm of frequency-specific LFP oscillations using a generalized mathematical model of spontaneous and stimulation-evoked LFP activity, and a subject-specific model of neural dynamics in the pallidum of a Parkinson’s disease patient. We leveraged convex and mixed-integer optimization tools to identify the pulse patterns, and employed constraints on the pulse frequency and amplitude that are required to keep electrical stimulation within its safety envelope. Our analysis revealed that a combination of phase, amplitude, and frequency pulse modulation is needed to attain optimal suppression or amplification of the targeted oscillations. Phase modulation is sufficient to modulate oscillations with a constant amplitude envelope. To attain optimal modulation for oscillations with a time-varying envelope, a trade-off between frequency and amplitude pulse modulation is needed. The optimized pulse sequences identified here were invariant to changes in the dynamics of stimulation-evoked neural activity, including the damping and natural frequency or complexity (i.e., generalized vs. patient-specific model). Our results reveal the structure of pulse sequences that can be used in closed-loop brain stimulation devices to control neural activity in real-time.Significance StatementThis computational study reveals the structure of electrical pulse sequences that optimally modulate spontaneous, synaptic-related neural oscillations measured using local field potentials (LFPs). We considered constraints on the pulse amplitude and frequency, relevant to keep stimulation pulses within the safety envelope. Our mathematical analysis indicate that these optimized pulse sequences are invariant to changes in the studied neural dynamics, and a trade-off between amplitude and frequency pulse modulation is critical when the pulse amplitude is constrained. The pulse sequences identified here provide the rationale for the development of closed-loop neuromodulation systems that employ stimulation-evoked responses to control neural activity. These closed-loop systems will be key to characterize the role of neural activity in brain function and ultimately advance personalized neuromodulation devices.